Buch, Englisch, 512 Seiten, Format (B × H): 156 mm x 235 mm, Gewicht: 907 g
Reihe: Mathematical Modeling
Buch, Englisch, 512 Seiten, Format (B × H): 156 mm x 235 mm, Gewicht: 907 g
Reihe: Mathematical Modeling
ISBN: 978-0-8493-8331-1
Verlag: CRC Press
Addressed to engineers, scientists, and applied mathematicians, this book explores the fundamental aspects of mathematical modelling in applied sciences and related mathematical and computational methods. After providing the general framework needed for mathematical modelling-definitions, classifications, general modelling procedures, and validation methods-the authors deal with the analysis of discrete models. This includes modelling methods and related mathematical methods. The analysis of models is defined in terms of ordinary differential equations. The analysis of continuous models, particularly models defined in terms of partial differential equations, follows. The authors then examine inverse type problems and stochastic modelling. Three appendices provide a concise guide to functional analysis, approximation theory, and probability, and a diskette included with the book includes ten scientific programs to introduce the reader to scientific computation at a practical level.
Zielgruppe
Professional
Fachgebiete
Weitere Infos & Material
PrefaceMathematical ModellingIntroductionDefinition of Mathematical ModellingClassification of Mathematical ModellingModelling MethodsValidation of Mathematical ModelsMathematical Modelling as a ScienceDiscrete ModelsPlan of Chapter 2About Mathematical ModellingMathematical Formulation of ProblemsOn Existence, Uniqueness and ContinuityLinear SystemsStability and LinearizationFrom Bifurcation to ChaosNumerical Methods for Initial Value ProblemsScientific ProgramsContinuous ModelsIntroductionMathematical ModellingEquilibrium Equation for the Vibration of an Elastic StringMathematical Models of Continuum MechanicsMathematical Models of ElectromagnetismDirect Simulation Models in BiologyClassification and CharacteristicsMathematical Formulation of ProblemsFinite Difference MethodsThe Collocation MethodDecomposition of DomainsApplications and Scientific ProgramsInverse and Stochastic ProblemsInverse Problems and Stochastic ModelsClassification of Inverse ProblemsSolution by Decomposition of DomainsSolution by Minimization TechniquesMathematical Modelling and StochasticityClassification of Discrete Stochastic ModelsClassification of Continuous Stochastic ModelsModelling and Solution of ProblemsStochastic Aspects and Inverse ProblemsKinetic ModelsApplicationDiscussion and DevelopmentsScientific ProgramsAppendix 1. Functional Spaces and Fixed Point TheoremsAppendix 2. Interpolation and ApproximationAppendix 3. Random VariablesReferencesSubjects Index